Abstract: In construction of concrete dams, raising the height of certain built dams appropriately is an important means of improving utilization efficiency and preventing disasters, but the joint interfaces of new-old concrete are prone to slide and become a weak plane that is sensitive to temperature. To solve this problem, we have developed a new contact sliding mode of multiple slices to analyze the slide stability of dam heightening. This paper uses a rigid limit equilibrium method to derive a calculation formula for three sliding interfaces, considering two calculation models of uplift water pressure. We applied this formula to the Danjiangkou dam heightening of the mid-route south-to-north water transfer project, and successfully rechecked the safety factors against sliding for the new-old concrete joints in the right dam blocks No. 1 and 7. For the recheck calculation, we also derived a corresponding formula for the case of N sliding interfaces. The results presented would help stability analysis for dam heightening in similar cases.